I've just tried two servers and both loaded all skins and mods really quickly. No errors. I'll try a few more servers tomorrow during the day and report back. So far so good...fingers crossed.
I've since tried 4 or 5 servers and all have been loading skins and mods quickly without error. For me at least, this setting change appears to have cured the problem. It would be good to hear from other people with BT as their ISP if their problem has also been resolved.
If there is any change I'll post back, but thank you for at least looking into it and trying something, it's certainly made getting onto a server better for me.
Some of the others seem to have no problem now. I'm not sure what the reason is. I have doubts that it was my change to Cloudflare settings as you still had the problem after I made that change. I believe Cloudflare settings take effect quickly, so it probably can't be explained by a delay. I wonder if our users' ISPs just sorted out their issue, overactive blocking or whatever it was.
I think I will have to restore the Cloudflare setting at some point and we'll see if that has any negative effect.